How do you simplify #4sinx + 5sin6x #?

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Answer 1 · 2018-06-17T17:36:42

#"The Exp."=2sinx{2+5cosx(3-16sin^2x+16sin^4x)}#.

#"The Expression"=4sinx+5sin6x#,

#=4sinx+5(2color(red)(sin3x)color(blue)(cos3x))#,

#=4sinx+10color(red)((3sinx-4sin^3x))color(blue)((4cos^3x-3cosx))#,

#=4sinx+10{sinx(3-4sin^2x)}{cosx(4cos^2x-3)}#,

#=4sinx+10sinxcosx(3-4sin^2x)(4cos^2x-3)#,

#=4sinx+10sinxcosx(3-4sin^2x){4(1-sin^2x)-3}#,

#=4sinx+10sinxcosx(3-4sin^2x)(1-4sin^2x)#,

#=4sinx+10sinxcosx(3-16sin^2x+16sin^4x)#.

#rArr"The Exp."=2sinx{2+5cosx(3-16sin^2x+16sin^4x)}#.